{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "038d3b26-49e3-4b1a-a1fa-de586f0586c9",
   "metadata": {},
   "source": [
    "# Optional Lab: Gradient Descent for Logistic Regression"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "235f7838-877e-4d98-96f3-f1d40a4e1c20",
   "metadata": {},
   "source": [
    "## Goals\n",
    "In this lab, you will:\n",
    "- update gradient descent for logistic regression.\n",
    "- explore gradient descent on a familiar data set"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "c8da956d-cc4e-4e5c-86a4-e8c3cfb8aff8",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-06-17T12:18:30.073007Z",
     "start_time": "2022-06-17T12:18:28.561860Z"
    }
   },
   "outputs": [],
   "source": [
    "import copy, math\n",
    "import numpy as np\n",
    "%matplotlib widget\n",
    "import matplotlib.pyplot as plt\n",
    "from lab_utils_common import  dlc, plot_data, plt_tumor_data, sigmoid, compute_cost_logistic\n",
    "from plt_quad_logistic import plt_quad_logistic, plt_prob\n",
    "plt.style.use('./deeplearning.mplstyle')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a6fde024-9a82-47bf-a48c-d5c67af69118",
   "metadata": {},
   "source": [
    "## Data set \n",
    "Let's start with the same two feature data set used in the decision boundary lab."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "62794deb-122c-4ba4-b04f-5b3bec3e8304",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-06-17T12:18:30.089011Z",
     "start_time": "2022-06-17T12:18:30.077010Z"
    }
   },
   "outputs": [],
   "source": [
    "X_train = np.array([[0.5, 1.5], [1,1], [1.5, 0.5], [3, 0.5], [2, 2], [1, 2.5]])\n",
    "y_train = np.array([0, 0, 0, 1, 1, 1])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bcc048b6-b74d-43d8-8f17-e083d33fdf23",
   "metadata": {},
   "source": [
    "As before, we'll use a helper function to plot this data. The data points with label $y=1$ are shown as red crosses, while the data points with label $y=0$ are shown as blue circles."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "37f852de-11c0-4e6f-bc07-663728144a9d",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-06-17T12:18:30.613128Z",
     "start_time": "2022-06-17T12:18:30.101017Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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exev1cuLECfKuLdp96tQpXC4XHo+H3bt3s2jRIjvKCXr+Hkgabt3+ezOsLIexm+CLb8JrHRYQWDAZvppka2kiUWvIX/z2X+fgwRLrmpXOzP08/HI2JA4zvmuRAa2v770hf51oRhIczYNNx6xL9esvQbwDMm+Hf0mF3C9ArC7TF+mxId9TEZHO6TJ9ERkQFCoiYpRCRUSMUqiIiFEKFRExSqEiIkYpVETEKIWKiBilUBERoxQqImKUQkVEjFKoiIhRChURMUqhIiJGKVRExCiFiogYpVAREaMUKiJi1JD/jtpI+KQZth2Hbe/CXxthhAOyJ8JTqXDPrZGuTqR/9B21Nqs6Bw+VwJkuvr1/9T3ww/s6XzFRxE76jtoo8P4lmF3cdaAAvHIY/v2P9tUkYppCxUb/uxI+vmLddsbDhix4Nx/eyoVZE9sf93+q4MNugkdkIFOo2ORSMxS9237/1w/A//wyTHHCrH+A0ocg49p4SksrvFEXmTpF+suWUMnJycHpdOL3+0O2+/1+vF4vbreb/Pz84LrKg1HtBbh81bo9xRnaMwFrbeeO6zVXnrOvNhGTbAmV0tJSMjIyOt0+depUysvLSUtLo6SkxI5yIuJqh+Hw4Y7OB2JHONpvtw7o4XORrkX09Ke2tjYYNtOmTePYsWORLCespjjBcS1Iaj6GP30U2h4IwNbj7fdTxthXm4hJEQ2VQCCAw9H+5zlmEM+jJo2AeV9ov/9YKZScsnokpxthZTnsabDaYoBlX4pElSL9F9GL31JSUqiqquKBBx6gsrKS1NTUSJYTdv/6P+B3f4ErV+H9T2BuibX4+/WnOsu/BHeNjkyNIv1lS09l6dKlHD16FK/Xy4kTJ8jLywOsAdyamhrcbjeHDx9mzpw5dpQTMRlJ8Kt/ghEdovz6QHnkTvjp/fbWJWKSrqiNgBOX4CfV1hjKR5etsZb7x8PTafDYXVbvRSTS+vreU6hE2GU/xDsUJDLw9PW9pw8URthwvQIyyOiKWhExSqEiIkYpVETEKIWKiBilUBERoxQqImKUQkVEjFKoiIhRChURMUqhIiJGKVRExCiFiogYpVAREaMUKiJilEJFRIxSqIiIUQoVETFK3zs2BHzaAm++B7734INPYXQ85EyCFSkwfmSkq4tCdXWQnNzz7UOMeiqD3H9+CJOLYEUZvHXaWsjswAfwb4fgC9vg50cjXWGUKSiA1FTw+UK3+3zW9oKCyNQ1gKinMogd/RhmF8MnXSxR3dwK/1wOiXHg/aK9tUWlggJYvdq67fVaP/PyrEDxeqG1tb191arI1DgA6Nv0B7FHfg87T1q3xyTAS1+Fr0+EoxdgXZX1EyBpOPx1MSQ4unwqqauzeiJXr7Zvi42F3FwoLrYCpY3DAUeORP2pUF/fezr9GaRON0Lxqfb7ux6C1V+BrybBwi/CgUdhfKLVdu4y/PZERMqMHsnJsG2bFSRtWlth587QQImNtR4X5YHSH7aEit/vx+v14na7yc/Pp6UltD/udDrxeDx4PB6KiorsKGnQqzzXvvph5h0w/bbQdmcCLO3w//4/z9pXW9TKy4Pt20ODpaPYWKv92gqcQ5UtoVJaWsrUqVMpLy8nLS2NkpKSkPb09HTKysooKysjPz/fjpIGvZYOfzyd8Z0/5paEzh8v3cjLs055OpObO+QDBWwKldraWjIyMgCYNm0ax44dC2mvr6/H5XLh9Xppamqyo6RB7+4Op8D7GuDsp6HtgQD8v/c6f7x0w+ezxlA6U1x846zQEGRLqAQCARyO9lHAmJjQNT7PnDlDRUUF06dPZ/PmzXaUNOh9eRx89Vbr9uWrMK8U/nzeun+myZpirvrIup/gAO/dESkzunSc5elMa6vVPsSDxZZQSUlJoaqqCoDKykpSUlKCbY2NjcExlsTERBISEjp9DumdmBj4t2nt9w9+CPf8EsZtggmFsKm2ve3pVLh1hP01RpW6Oli48MZB2Xnzbhy8XbjQevwQZUuo5OTkUFNTg9vt5vDhw8yZM4e8a+eep06dwuVy4fF42L17N4sWLbKjpCFh3p2wISt028dXQu8/MRnWz7CvpqiVnAzr17ffbxuU3bHjxsHb9euH9OyPrlMZAt75ADb8GX77fvuAbNYd8Gw6LJgMsTHd/750UFAAL75oTRt3HJT1+aweyvr1g+bCt76+9xQqQ8iVq3DhCowaZv2TPhoin/1RqIiIUbqiVkQGBIWKiBilUBERoxQqImKUQkVEjFKoiIhRChURMUqhIiJGKVRExCiFiogYpVAREaMUKiJilEJFRIxSqIiIUQoVETFKoSIiRilURMQohYqIGKVQERGjFCoiYpRCRUSMUqiIiFFxduzE7/ezZMkSTp8+zcSJE9myZQvDhg27adv1Oi4ZICIDky09ldLSUqZOnUp5eTlpaWmUlJT0qE1Eoo8toVJbW0tGRgYA06ZN49ixYz1qE5HoY8vpTyAQwOFwBO/HxMT0qA20KqFItLGlp5KSkkJVVRUAlZWVpKSk9KhNRKKPLWspdxyMHT9+PFu3bmXRokX4fL5O27oaqBWRgW/AL9AuItFlQF2n4vf78Xq9uN1u8vPzaWlp6VFbOPYH1niOx+PB4/FQVFTU7/3l5OTgdDrx+/29qsP0/sD8sQEcP34cl8vFjBkzmD9/flhfv+72BeaP7/z588yaNYvs7Gyys7NpaGgItoXj9etufxCe1w/A5/MxZcqUkG29Pb4BFSp2Tz3f7DnT09MpKyujrKyM/Px8I/trm+nqTR2m9wfmjw1gwoQJ7Nmzh4MHDzJ+/PjgWFlbLSaPsbt9gfnjczqd7Nq1i3379uF2uzl8+HCwLRyvX3f7g/C8fr/61a84e/Ysd9xxR8j23h7fgAoVu6eeb/ac9fX1uFwuvF4vTU1N/d5fX+sIh3Ac26hRo0hISCAQCFBfXx/yF8/0MXa3LzB/fHFxccTFxZGZmcmhQ4eYPXt2sC0cr193+wPzx7djxw5Onz7Nt7/97Rvaent8AypU+jP1bHp/AGfOnKGiooLp06ezefPmfu+vr3WEQziPbfXq1Sxbtoxx48YFt4XrGDvbF4Tv+A4cOEBubi5btmwJbgvn69fZ/sD88f3hD39g586deDweqquree6554JtvT2+ARUqdk89d/ecjY2NwXPHxMREEhIS+r2/vtQRDuE6tubmZlauXElWVhYLFiwIaTN9jN3tKxzHd+HCBZqbmwHrTdVxXCEcr193+wvH8b366qvB06n09HQ2bNgQbOv18QUGkJaWlkB+fn7g/vvvDzz55JOB5ubmwJNPPtllWzj3V1NTE7j33nsDbrc7MH/+/MBnn33W7/0tWbIkkJSUFHjiiScC9fX1YT227vYXjmMLBAKBLVu2BCZOnBhwu90Bt9sd2Lx5c9iOsbt9heP4qqqqAvfdd1/A7XYHHnnkkUBjY2NYX7/u9heu169NVlZWIBAI9Pn4NKUsIkYNqNMfEYl+ChURMUqhIiJGKVRExCiFiogYpVAREaMUKmLMCy+8wKOPPhq8v2bNGmbNmmXsA5ISHXSdihhz/vx5Jk+eTFlZGQcPHuSnP/0pFRUV+va+IcaWr5OUoWHcuHE899xzLF68mIsXL4YEytq1a3n77be5/fbbKSwsJDExMcLVSrjo9EeMysjIoLq6mnXr1jFp0iQAampqqK+vZ//+/XzjG99g06ZNEa5SwkmhIsZUV1fz1FNPsWTJkpDg2L9/P3PmzAFgzpw5VFRURKpEsYFCRYxoaGggNzeXjRs38uqrr1JdXU1ZWRlgfeK27TTI6XTy8ccfR7BSCTeFivTbpUuXePDBB3n++ed5+OGHSUxMZM2aNaxduxaAMWPGBFeXvHjxImPHjo1kuRJmmv2RsGsbYykqKuJnP/sZV65c4dlnn410WRImmv2RsEtPT+fzn/88M2fO5LbbbqOwsDDSJUkYqaciIkZpTEVEjFKoiIhRChURMUqhIiJGKVRExCiFiogYpVAREaMUKiJi1H8D/wCOMvcWgXcAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 288x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig,ax = plt.subplots(1,1,figsize=(4,4))\n",
    "plot_data(X_train, y_train, ax)\n",
    "\n",
    "ax.axis([0, 4, 0, 3.5])\n",
    "ax.set_ylabel('$x_1$', fontsize=12)\n",
    "ax.set_xlabel('$x_0$', fontsize=12)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "449f22e4-eb90-4810-b0d1-c8ae7ecacba2",
   "metadata": {},
   "source": [
    "## Logistic Gradient Descent\n",
    "<img align=\"right\" src=\"./images/C1_W3_Logistic_gradient_descent.png\"     style=\" width:400px; padding: 10px; \" >\n",
    "\n",
    "Recall the gradient descent algorithm utilizes the gradient calculation:\n",
    "$$\\begin{align*}\n",
    "&\\text{repeat until convergence:} \\; \\lbrace \\\\\n",
    "&  \\; \\; \\;w_j = w_j -  \\alpha \\frac{\\partial J(\\mathbf{w},b)}{\\partial w_j} \\tag{1}  \\; & \\text{for j := 0..n-1} \\\\ \n",
    "&  \\; \\; \\;  \\; \\;b = b -  \\alpha \\frac{\\partial J(\\mathbf{w},b)}{\\partial b} \\\\\n",
    "&\\rbrace\n",
    "\\end{align*}$$\n",
    "\n",
    "Where each iteration performs simultaneous updates on $w_j$ for all $j$, where\n",
    "$$\\begin{align*}\n",
    "\\frac{\\partial J(\\mathbf{w},b)}{\\partial w_j}  &= \\frac{1}{m} \\sum\\limits_{i = 0}^{m-1} (f_{\\mathbf{w},b}(\\mathbf{x}^{(i)}) - y^{(i)})x_{j}^{(i)} \\tag{2} \\\\\n",
    "\\frac{\\partial J(\\mathbf{w},b)}{\\partial b}  &= \\frac{1}{m} \\sum\\limits_{i = 0}^{m-1} (f_{\\mathbf{w},b}(\\mathbf{x}^{(i)}) - y^{(i)}) \\tag{3} \n",
    "\\end{align*}$$\n",
    "\n",
    "* m is the number of training examples in the data set      \n",
    "* $f_{\\mathbf{w},b}(x^{(i)})$ is the model's prediction, while $y^{(i)}$ is the target\n",
    "* For a logistic regression model  \n",
    "    $z = \\mathbf{w} \\cdot \\mathbf{x} + b$  \n",
    "    $f_{\\mathbf{w},b}(x) = g(z)$  \n",
    "    where $g(z)$ is the sigmoid function:  \n",
    "    $g(z) = \\frac{1}{1+e^{-z}}$   \n",
    "    \n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "af9a2ac9-0ac2-4eb1-9c83-a2b434c9dcb8",
   "metadata": {},
   "source": [
    "### Gradient Descent Implementation\n",
    "The gradient descent algorithm implementation has two components: \n",
    "- The loop implementing equation (1) above. This is `gradient_descent` below and is generally provided to you in optional and practice labs.\n",
    "- The calculation of the current gradient, equations (2,3) above. This is `compute_gradient_logistic` below. You will be asked to implement this week's practice lab.\n",
    "\n",
    "#### Calculating the Gradient, Code Description\n",
    "Implements equation (2),(3) above for all $w_j$ and $b$.\n",
    "There are many ways to implement this. Outlined below is this:\n",
    "- initialize variables to accumulate `dj_dw` and `dj_db`\n",
    "- for each example\n",
    "    - calculate the error for that example $g(\\mathbf{w} \\cdot \\mathbf{x}^{(i)} + b) - \\mathbf{y}^{(i)}$\n",
    "    - for each input value $x_{j}^{(i)}$ in this example,  \n",
    "        - multiply the error by the input  $x_{j}^{(i)}$, and add to the corresponding element of `dj_dw`. (equation 2 above)\n",
    "    - add the error to `dj_db` (equation 3 above)\n",
    "\n",
    "- divide `dj_db` and `dj_dw` by total number of examples (m)\n",
    "- note that $\\mathbf{x}^{(i)}$ in numpy `X[i,:]` or `X[i]`  and $x_{j}^{(i)}$ is `X[i,j]`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "2c90c465-5b12-46cc-aa04-41b457c24bed",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-06-17T12:18:30.644137Z",
     "start_time": "2022-06-17T12:18:30.619133Z"
    }
   },
   "outputs": [],
   "source": [
    "def compute_gradient_logistic(X, y, w, b): \n",
    "    \"\"\"\n",
    "    Computes the gradient for linear regression \n",
    " \n",
    "    Args:\n",
    "      X (ndarray (m,n): Data, m examples with n features\n",
    "      y (ndarray (m,)): target values\n",
    "      w (ndarray (n,)): model parameters  \n",
    "      b (scalar)      : model parameter\n",
    "    Returns\n",
    "      dj_dw (ndarray (n,)): The gradient of the cost w.r.t. the parameters w. \n",
    "      dj_db (scalar)      : The gradient of the cost w.r.t. the parameter b. \n",
    "    \"\"\"\n",
    "    m,n = X.shape\n",
    "    dj_dw = np.zeros((n,))                           #(n,)\n",
    "    dj_db = 0.\n",
    "\n",
    "    for i in range(m):\n",
    "        f_wb_i = sigmoid(np.dot(X[i],w) + b)          #(n,)(n,)=scalar\n",
    "        err_i  = f_wb_i  - y[i]                       #scalar\n",
    "        for j in range(n):\n",
    "            dj_dw[j] = dj_dw[j] + err_i * X[i,j]      #scalar\n",
    "        dj_db = dj_db + err_i\n",
    "    dj_dw = dj_dw/m                                   #(n,)\n",
    "    dj_db = dj_db/m                                   #scalar\n",
    "        \n",
    "    return dj_db, dj_dw  "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4c4e5f34-fd61-4640-b0ee-0f6c6641012d",
   "metadata": {},
   "source": [
    "Check the implementation of the gradient function using the cell below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "10deeb4d-bdab-4a9f-aa41-49bab8f3156e",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-06-17T12:18:30.675142Z",
     "start_time": "2022-06-17T12:18:30.648138Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "dj_db: 0.49861806546328574\n",
      "dj_dw: [0.498333393278696, 0.49883942983996693]\n"
     ]
    }
   ],
   "source": [
    "X_tmp = np.array([[0.5, 1.5], [1,1], [1.5, 0.5], [3, 0.5], [2, 2], [1, 2.5]])\n",
    "y_tmp = np.array([0, 0, 0, 1, 1, 1])\n",
    "w_tmp = np.array([2.,3.])\n",
    "b_tmp = 1.\n",
    "dj_db_tmp, dj_dw_tmp = compute_gradient_logistic(X_tmp, y_tmp, w_tmp, b_tmp)\n",
    "print(f\"dj_db: {dj_db_tmp}\" )\n",
    "print(f\"dj_dw: {dj_dw_tmp.tolist()}\" )"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "98f0b5af-8ecf-412d-9e8b-437ed22631fb",
   "metadata": {},
   "source": [
    "**Expected output**\n",
    "``` \n",
    "dj_db: 0.49861806546328574\n",
    "dj_dw: [0.498333393278696, 0.49883942983996693]\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e6e58c2b-e524-4e14-ad68-542f56ab2e97",
   "metadata": {},
   "source": [
    "#### Gradient Descent Code \n",
    "The code implementing equation (1) above is implemented below. Take a moment to locate and compare the functions in the routine to the equations above."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "bf185b79-9d84-423a-a4d9-5e0d188f0643",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-06-17T12:18:30.691145Z",
     "start_time": "2022-06-17T12:18:30.679143Z"
    }
   },
   "outputs": [],
   "source": [
    "def gradient_descent(X, y, w_in, b_in, alpha, num_iters): \n",
    "    \"\"\"\n",
    "    Performs batch gradient descent\n",
    "    \n",
    "    Args:\n",
    "      X (ndarray (m,n)   : Data, m examples with n features\n",
    "      y (ndarray (m,))   : target values\n",
    "      w_in (ndarray (n,)): Initial values of model parameters  \n",
    "      b_in (scalar)      : Initial values of model parameter\n",
    "      alpha (float)      : Learning rate\n",
    "      num_iters (scalar) : number of iterations to run gradient descent\n",
    "      \n",
    "    Returns:\n",
    "      w (ndarray (n,))   : Updated values of parameters\n",
    "      b (scalar)         : Updated value of parameter \n",
    "    \"\"\"\n",
    "    # An array to store cost J and w's at each iteration primarily for graphing later\n",
    "    J_history = []\n",
    "    w = copy.deepcopy(w_in)  #avoid modifying global w within function\n",
    "    b = b_in\n",
    "    \n",
    "    for i in range(num_iters):\n",
    "        # Calculate the gradient and update the parameters\n",
    "        dj_db, dj_dw = compute_gradient_logistic(X, y, w, b)   \n",
    "\n",
    "        # Update Parameters using w, b, alpha and gradient\n",
    "        w = w - alpha * dj_dw               \n",
    "        b = b - alpha * dj_db               \n",
    "      \n",
    "        # Save cost J at each iteration\n",
    "        if i<100000:      # prevent resource exhaustion \n",
    "            J_history.append( compute_cost_logistic(X, y, w, b) )\n",
    "\n",
    "        # Print cost every at intervals 10 times or as many iterations if < 10\n",
    "        if i% math.ceil(num_iters / 10) == 0:\n",
    "            print(f\"Iteration {i:4d}: Cost {J_history[-1]}   \")\n",
    "        \n",
    "    return w, b, J_history         #return final w,b and J history for graphing\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "135780cf-214a-4d5e-9c11-28eabe9dc42f",
   "metadata": {},
   "source": [
    "Let's run gradient descent on our data set."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "52815246-1d10-4fad-9a87-eeb3a58f0176",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-06-17T12:18:35.623183Z",
     "start_time": "2022-06-17T12:18:30.696147Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Iteration    0: Cost 0.684610468560574   \n",
      "Iteration 1000: Cost 0.1590977666870457   \n",
      "Iteration 2000: Cost 0.08460064176930078   \n",
      "Iteration 3000: Cost 0.05705327279402531   \n",
      "Iteration 4000: Cost 0.04290759421682   \n",
      "Iteration 5000: Cost 0.03433847729884557   \n",
      "Iteration 6000: Cost 0.02860379802212006   \n",
      "Iteration 7000: Cost 0.02450156960879306   \n",
      "Iteration 8000: Cost 0.02142370332569295   \n",
      "Iteration 9000: Cost 0.019030137124109114   \n",
      "\n",
      "updated parameters: w:[5.28 5.08], b:-14.222409982019837\n"
     ]
    }
   ],
   "source": [
    "w_tmp  = np.zeros_like(X_train[0])\n",
    "b_tmp  = 0.\n",
    "alph = 0.1\n",
    "iters = 10000\n",
    "\n",
    "w_out, b_out, _ = gradient_descent(X_train, y_train, w_tmp, b_tmp, alph, iters) \n",
    "print(f\"\\nupdated parameters: w:{w_out}, b:{b_out}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3466baef-bfc5-418c-a903-0a80c843ef61",
   "metadata": {},
   "source": [
    "#### Let's plot the results of gradient descent:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "d1d946da-f5a2-404b-aaf3-ad9306581e74",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-06-17T12:18:36.585993Z",
     "start_time": "2022-06-17T12:18:35.625183Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x288 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig,ax = plt.subplots(1,1,figsize=(5,4))\n",
    "# plot the probability \n",
    "plt_prob(ax, w_out, b_out)\n",
    "\n",
    "# Plot the original data\n",
    "ax.set_ylabel(r'$x_1$')\n",
    "ax.set_xlabel(r'$x_0$')   \n",
    "ax.axis([0, 4, 0, 3.5])\n",
    "plot_data(X_train,y_train,ax)\n",
    "\n",
    "# Plot the decision boundary\n",
    "x0 = -b_out/w_out[1]\n",
    "x1 = -b_out/w_out[0]\n",
    "ax.plot([0,x0],[x1,0], c=dlc[\"dlblue\"], lw=1)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f2af4d30-b49d-4062-8820-87558039cbc8",
   "metadata": {},
   "source": [
    "In the plot above:\n",
    " - the shading reflects the probability y=1 (result prior to decision boundary)\n",
    " - the decision boundary is the line at which the probability = 0.5\n",
    " "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7d17c626-93e8-49f5-ba04-0f70cad94174",
   "metadata": {},
   "source": [
    "## Another Data set\n",
    "Let's return to a one-variable data set. With just two parameters, $w$, $b$, it is possible to plot the cost function using a contour plot to get a better idea of what gradient descent is up to."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "704c2a67-3e63-4b2b-90d8-170705920e2c",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-06-17T12:18:36.601996Z",
     "start_time": "2022-06-17T12:18:36.588995Z"
    }
   },
   "outputs": [],
   "source": [
    "x_train = np.array([0., 1, 2, 3, 4, 5])\n",
    "y_train = np.array([0,  0, 0, 1, 1, 1])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1e8757f1-af25-4ec8-87e3-13c285ee80fb",
   "metadata": {},
   "source": [
    "As before, we'll use a helper function to plot this data. The data points with label $y=1$ are shown as red crosses, while the data points with label $y=0$ are shown as black circles."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "ed37764e-ff84-44df-beca-12d83803782d",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-06-17T12:18:36.726621Z",
     "start_time": "2022-06-17T12:18:36.603998Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 288x216 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig,ax = plt.subplots(1,1,figsize=(4,3))\n",
    "plt_tumor_data(x_train, y_train, ax)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a4151740-e04f-4705-a9bb-5529811f58f6",
   "metadata": {},
   "source": [
    "In the plot below, try:\n",
    "- changing $w$ and $b$ by clicking within the contour plot on the upper right.\n",
    "    - changes may take a second or two\n",
    "    - note the changing value of cost on the upper left plot.\n",
    "    - note the cost is accumulated by a loss on each example (vertical dotted lines)\n",
    "- run gradient descent by clicking the orange button.\n",
    "    - note the steadily decreasing cost (contour and cost plot are in log(cost) \n",
    "    - clicking in the contour plot will reset the model for a new run\n",
    "- to reset the plot, rerun the cell"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "053a8687-9426-4468-b52e-9a68a81e5b4f",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-06-17T12:18:38.724589Z",
     "start_time": "2022-06-17T12:18:36.728623Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x432 with 5 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "w_range = np.array([-1, 7])\n",
    "b_range = np.array([1, -14])\n",
    "quad = plt_quad_logistic( x_train, y_train, w_range, b_range )"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ab3a295b-682e-4d6d-b242-93d0514b0e63",
   "metadata": {},
   "source": [
    "## Congratulations!\n",
    "You have:\n",
    "- examined the formulas and implementation of calculating the gradient for logistic regression\n",
    "- utilized those routines in\n",
    "    - exploring a single variable data set\n",
    "    - exploring a two-variable data set"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "085a7f94-d988-4e2d-94ee-57888c302d77",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.10.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}
